Answer: [tex]45^{\circ}[/tex]
Step-by-step explanation:
[tex]\angle ABC[/tex] is formed by lines AB and BC.
- The slope of AB is [tex]\frac{2-5}{4-7}=-1[/tex]
- The slope of BC is [tex]\frac{2-2}{9-4}=0[/tex].
This means
[tex]\tan (\angle ABC)=\left|\frac{-1}{1}} \right|\\\tan(\angle ABC)=1[/tex]
From the diagram, we can tell that angle ABC is acute, so it measures [tex]\boxed{45^{\circ}}[/tex]
